Skip to main page content
Access keys NCBI Homepage MyNCBI Homepage Main Content Main Navigation
. 2012 May;8(5):e1002534.
doi: 10.1371/journal.pcbi.1002534. Epub 2012 May 31.

Thermodynamic Basis for the Emergence of Genomes During Prebiotic Evolution

Free PMC article

Thermodynamic Basis for the Emergence of Genomes During Prebiotic Evolution

Hyung-June Woo et al. PLoS Comput Biol. .
Free PMC article


The RNA world hypothesis views modern organisms as descendants of RNA molecules. The earliest RNA molecules must have been random sequences, from which the first genomes that coded for polymerase ribozymes emerged. The quasispecies theory by Eigen predicts the existence of an error threshold limiting genomic stability during such transitions, but does not address the spontaneity of changes. Following a recent theoretical approach, we applied the quasispecies theory combined with kinetic/thermodynamic descriptions of RNA replication to analyze the collective behavior of RNA replicators based on known experimental kinetics data. We find that, with increasing fidelity (relative rate of base-extension for Watson-Crick versus mismatched base pairs), replications without enzymes, with ribozymes, and with protein-based polymerases are above, near, and below a critical point, respectively. The prebiotic evolution therefore must have crossed this critical region. Over large regions of the phase diagram, fitness increases with increasing fidelity, biasing random drifts in sequence space toward 'crystallization.' This region encloses the experimental nonenzymatic fidelity value, favoring evolutions toward polymerase sequences with ever higher fidelity, despite error rates above the error catastrophe threshold. Our work shows that experimentally characterized kinetics and thermodynamics of RNA replication allow us to determine the physicochemical conditions required for the spontaneous crystallization of biological information. Our findings also suggest that among many potential oligomers capable of templated replication, RNAs may have evolved to form prebiotic genomes due to the value of their nonenzymatic fidelity.

Conflict of interest statement

The authors have declared that no competing interests exist.


Figure 1
Figure 1. Kinetics and thermodynamics of RNA replication.
A: Single-molecule kinetics. B: Population dynamics.
Figure 2
Figure 2. Variations of inverse fidelity and mean base incorporation rate among polymerases.
See Tables 1 and 2 for the references. Arrows show the likely direction of evolutionary changes.
Figure 3
Figure 3. Numerical tests of mean field theory.
A: Three components of formula image as functions of formula image for a symmetric template model for which the mean field theory is exact. The rates were given by formula image, formula image, formula image, and formula image for formula imageA, U, G, C. Lines are from Eq. (40). Symbols are from numerical simulations. B: Test of site-independence for the sequence distribution, Eq. (35), with pol formula image rates (Table 2F). All symbols were calculated from numerical simulations. C–D: Mean velocity (C) and error rate (D) for the pol formula image kinetics, both with full experimental kinetics (Table 2) and Jukes-Cantor version (JC) derived from the full kinetic set. Symbols are from simulations, which verify that for JC kinetics the mean field prediction is exact.
Figure 4
Figure 4. Single-molecule elongation properties as functions of .
A–B: Mean RNA sequence elongation velocity formula image in units of formula image (A) and mean error rate (B) with nonenzymatic, R18 ribozyme, and poliovirus formula image kinetics, which show supercritical, near-critical, and subcritical behaviors, respectively. Green arrows indicate discontinuous jumps for poliovirus. The diamonds denote formula image values using the poliovirus sequence (instead of random sequences for others), and the triangles indicate formula image for poliovirus. C–D: Mean elongation velocity (C) and mean error rate (D) with increasing fidelity based on rescaled nonenzymatic kinetics.
Figure 5
Figure 5. Thermodynamic phase diagrams of RNA replication.
A–B: The formula image-formula image diagrams with color levels and contours (black dashed lines) representing formula image (A) and formula image (B). The black solid lines show the spinodal terminated by the critical point (filled circles). The red solid lines show the L-C transition for formula image and formula image, which meets the spinodal at the triple point (open circles). The white dashed lines show the boundary of formula image region (smaller formula image side). The green dashed lines show the analogous region of formula image values for starvation processes (formula image). The vertical lines show the location of the nonenzymatic formula image value. C–D: The formula image-formula image and formula image-formula image diagrams. The green dashed lines represent the formula image boundary. The blue dotted lines give the maximum and minimum formula image and formula image, respectively, and the red dotted line in D denotes the maximum error rate at equilibrium. The fitness formula image is in units of formula image.
Figure 6
Figure 6. Dependence of mean fitness on fidelity.
A: Mean fitness as a function of formula image at constant formula image. The slope formula image is negative below a threshold formula image for each formula image (white dashed lines in Figure 5A,B and green dashed lines in Figure 5C,D, respectively). The discontinuous jump for formula image and the cusps at smaller formula image values correspond to G-L and L-C transitions, respectively. B: Mean fitness averaged over starvation processes (formula image) for different initial thermodynamic force formula image (see Figure 10). The slope formula image is negative below a threshold formula image for each formula image (green dotted lines in Figure 5A,B). Vertical lines represent the nonenzymatic fidelity. The fitness formula image is in units of formula image.
Figure 7
Figure 7. Time dependence of master sequence frequency
formula image . Stochastic simulation results of the Eigen model (solid lines, averaged over 1000 trajectories) are compared with Eq. (54) (dotted line), where formula image is the fitness of mutants, for formula image and formula image. The initial condition was formula image.
Figure 8
Figure 8. Stationary frequency of master sequence.
Stochastic simulations results for the Eigen model are compared with formula image. The simulations were under the condition of (approximately) constant population size (formula image) using Eqs. (23). With formula image and formula image, the error threshold where formula image is at formula image. Error bars represent one standard deviations.
Figure 9
Figure 9. Crystallization of a genome.
Stochastic simulations were used with genome length formula image and mean base incorporation rate formula image. The initial population (formula image) contained random sequences and a single master sequence with relative fitness formula image. The inverse fidelity was given by Eq. (25) with formula image and formula image. A: Relative frequency of the master sequence (initially formula image). B: Average of the fractional Hamming distance (HD; formula image initially).
Figure 10
Figure 10. Variation of mean fitness during starvation processes.
The mean fitness is shown as a function of fractional population size formula image. The two formula image values (with formula image and formula image) illustrate typical behavior below and above the critical point. The C-L and L-G transitions are indicated for the subcritical case.
Figure 11
Figure 11. Sensitivity of fidelity threshold on equilibrium constant.
The dependence on formula image of the minimum formula image of starvation processes, for which formula image, are shown.

Similar articles

See all similar articles

Cited by 1 article


    1. Orgel LE. Prebiotic chemistry and the origin of the RNA world. Crit Rev Biochem Mol Biol. 2004;39:99–123. - PubMed
    1. Powner MW, Gerland B, Sutherland JD. Synthesis of activated pyrimidine ribonucleotides in prebiotically plausible conditions. Nature. 2009;459:239–242. - PubMed
    1. Hazen RM, Sverjensky DA. Mineral surfaces, geochemical complexities, and the origins of life. Cold Spring Harb Perspect Biol. 2010;2:a002162. - PMC - PubMed
    1. Mulkidjanian AY, Bychkov AY, Dibrova DV, Galperin MY, Koonin EV. Origin of first cells at terrestrial, anoxic geothermal fields. Proc Natl Acad Sci U S A. 2012;109:E821–E830. - PMC - PubMed
    1. Lincoln TA, Joyce GF. Self-sustained replication of an RNA enzyme. Science. 2009;323:1229–1232. - PMC - PubMed

Publication types